Combine avocado, lime juice, minced garlic, and cilantro in a food processor. Add sour cream and a pinch of salt. Blend until smooth, adjusting with water if needed. Set aside.

Heat grill or stovetop to medium-high. Char corn for about 2 minutes on each side until tender with char marks. Let cool, then slice off kernels.

Heat olive oil in a skillet over medium heat. Sauté onion and salt for 4-5 minutes until translucent. Add garlic, chili powder, cumin, and paprika, cooking for another minute.

Add drained black beans and vegetable broth to the skillet. Simmer for 5-7 minutes, mashing some beans for creaminess, finishing with lime juice, salt, and pepper to taste.

Assemble tostadas by spreading black bean filling on warmed shells. Top with charred corn and drizzle with avocado crema. Serve immediately.